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mathematical media
Dec. 19th, 2006 07:36 pmI have decided to read a mathematical textbook over the holidays, something I haven't done in a long time.
I keep wanting to click on terms that I don't recognize, to go to the definition.
Here's a useful programming/text-learning project: create a system that, given a mathematical document (LaTeX, PDF, scanned text), automatically turns it into a mathematical hypertext linking each technical term to its definition.
You can use a wiki to do the linking, as long as you have WikiTeX enabled to do the rendering. This should be a straightforward project if the original document is already in LaTeX. AFAIK, you can't put links on TeX-rendered images, but fortunately, terms that have definitions tend to be the kind that don't need any TeXing anyway.
For me, the next steps would be:
* variable substitution: the text lets the reader plug in values. This would be useful for understanding theorems.
* recognize whether a reader-given object satisfies a definition (along with a "WhyNot?" tool)
I think the main difficulty here is interpreting the written mathematical text into a formal language. Most people reading this are probably thinking about difficult questions, like which foundation they would choose. But the definitions that I have in mind could be decided with Prolog.
I should read OpenMath applications to see what people are up to. They have whole conferences on this stuff, so we should be seeing some progress in this area. I have to wonder why we don't yet see any interactive math books online (advanced, theorem-based math).
More ideas:
* interpreting diagrams as mathematical objects, which can (fail to) satisfy definitions.
I keep wanting to click on terms that I don't recognize, to go to the definition.
Here's a useful programming/text-learning project: create a system that, given a mathematical document (LaTeX, PDF, scanned text), automatically turns it into a mathematical hypertext linking each technical term to its definition.
You can use a wiki to do the linking, as long as you have WikiTeX enabled to do the rendering. This should be a straightforward project if the original document is already in LaTeX. AFAIK, you can't put links on TeX-rendered images, but fortunately, terms that have definitions tend to be the kind that don't need any TeXing anyway.
For me, the next steps would be:
* variable substitution: the text lets the reader plug in values. This would be useful for understanding theorems.
* recognize whether a reader-given object satisfies a definition (along with a "WhyNot?" tool)
I think the main difficulty here is interpreting the written mathematical text into a formal language. Most people reading this are probably thinking about difficult questions, like which foundation they would choose. But the definitions that I have in mind could be decided with Prolog.
I should read OpenMath applications to see what people are up to. They have whole conferences on this stuff, so we should be seeing some progress in this area. I have to wonder why we don't yet see any interactive math books online (advanced, theorem-based math).
More ideas:
* interpreting diagrams as mathematical objects, which can (fail to) satisfy definitions.